theorem :: FDIFF_7:49

for Z being open Subset of REAL st Z c= dom ((#Z 2) * (cos / sin)) & ( for x being Real st x in Z holds
sin . x <> 0 ) holds
( (#Z 2) * (cos / sin) is_differentiable_on Z & ( for x being Real st x in Z holds
(((#Z 2) * (cos / sin)) `| Z) . x = - ((2 * (cos . x)) / ((sin . x) #Z 3)) ) )